基于虚拟材料法的桁架固频极值求解  

Extremum Calculation of Natural Frequency for Truss Based on Virtual Material Method

作　　者：王庆[1] 徐斌[1] 赵普猛[1] 

机构地区：[1]西北工业大学力学与土木建筑学院,陕西西安710072

出　　处：《西北工业大学学报》2013年第3期498-502,共5页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(11072197);教育部博士点基金(2009102120024);西北工业大学基础研究基金(JC20120232)资助

摘　　要：基于固频约束时结构动力学拓扑优化的关键约束,提出了一种求解桁架结构固频极值的新方法——基于虚拟材料法的优化计算方法,从节点设计变量和杆件截面积两个层次进行灵敏度分析以进一步优化计算,将拟删除节点相对应的杆件材料特性进行重新赋值,通过极值求解算法以迭代计算得到固频极值。数值算例结果表明所提方法正确、有效。Because frequency constraint is the key constraint for dynamic topology optimization of truss,in this paper,a new method for extremum calculation of natural frequency for truss is put forward——an optimization method based on virtual material.It is optimized in two levels with sensitivity analysis;there are nodal design variables and cross-section area variables of truss elements,the bars related to the removed nodes being assigned new material properties;then the extremum of natural frequency is calculated with steepest descent method（SDM）.The results of a numerical example and their analysis show preliminarily that the proposed method is correct and effective.

关 键 词：固有频率 灵敏度分析 最速下降法 拓扑 桁架 固频极值 虚拟材料法 

分 类 号：O327[理学—一般力学与力学基础]